An incorrigibly bad individual. Example: The incorrigibles in the prison population are either lifers or habitual reoffenders.
Defective and impossible to materially correct or set aright. Example: The construction flaw is incorrigible; any attempt to amend it would cause a complete collapse.
Incurably depraved; not reformable. Example: His dark soul was too incorrigible to repent, even at his execution.
Impervious to correction by punishment or pain. Example: The imp is incorrigible: his bottom is still red from his last spanking when he plans the next prank.
Unmanageable.
Determined, unalterable, hence impossible to improve upon. Example: The laws of nature and mathematics are incorrigible.
Incurable.
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